Biomechanics Principles and Applications - Schneck and Bronzino

FIGURE 7.2 (a) Injury severity from blunt impact of human cadavers as a function of the maximum chest compression. (From Viano [1988], with permission.) (b) Severity of skeletal injury and incidence of internal organ injury as a function of maximum chest compression for blunt impacts of human cadavers. (From Viano [1988]. With permission.)

the maximum compression of the chest, as measured by the percentage change in the anteroposterior thickness of the body. A relationship between injury risk and compression involves energy stored by elastic deformation of the body. Stored energy Es by a spring representing the ribcage and soft tissues is related to the displacement integral of force: Es = ∫F dx. Force in a spring is proportional to deformation: F = kx, where k is a spring constant. Stored energy is Es = k∫x dx = 0.5kx2. Over a reasonable range, stored energy is proportional to deformation or compression, so Es ≈ C.

Tests with human volunteers showed that compression up to 20% during moderate-duration loading was fully reversible. Cadaver impacts with compression greater than 20% (Fig. 7.2a) an increase in rib fractures and internal organ injury as the compression increased to 40%. The deflection tolerance was originally set at 8.8 cm (3.5 in) for moderate but recoverable injury. This represents 39% compression. However, at this level of compression, multiple rib fractures and serious injury can occur, so a more conservative tolerance of 34% is used to avert the possibility of flail chest (Fig. 7.2b). This reduces the risk of direct loading on the heart, lungs, and internal organs by a loss of the protective function of the ribcage.

Viscous Injury

The velocity of body deformation is an important factor in impact injury. For example, when a fluidfilled organ is compressed slowly, energy can be absorbed by tissue deformation without damage. When loaded rapidly, the organ cannot deform fast enough, and rupture may occur without significant change in shape, even though the load is substantially higher than for the slow-loading condition.

The viscoelastic behavior of soft tissues is important when the velocity of deformation exceeds 3 m/s. For lower speeds, such as in slow crushing loads or for a belt-restrained occupant in a frontal crash, tissue compression is limited by elastic properties resisting skeletal and internal organ injury. For higher speeds of deformation, such as occupant loading by the door in a side impact or for an unrestrained occupant or pedestrian, maximum compression does not adequately address the viscous and inertial properties of the torso, nor the time of greatest injury risk. In these conditions, the tolerance to compression is progressively lower as the speed of deformation increases, and the velocity of deformation becomes a dominant factor in injury.

Insight on a rate-dependent injury mechanism came from over 20 years of research by Clemedson and Jonsson [1979] on high-speed impact and blast-wave exposures. The studies confirmed that tolerable compression inversely varied with the velocity of impact. The concept was studied further in relation to

FIGURE 7.4 (continued)

interface was added by Viano [1987] to evaluate protective padding. Chest structure is represented by a parallel Voigt and Maxwell spring-dashpot system that couples the sternal m2 and spinal m3 masses. When subjected to a blunt sternal impact, the model follows established force-deflection corridors. The biomechanical model is effective in studying compression and viscous responses. It also simulates military exposure to high-speed nonpenetrating projectiles (Fig. 7.6), even though the loading conditions are quite different from the cadaver database used to develop the model. This mechanical system characterizes the elastic, viscous, and inertial components of the torso.

The Hybrid III dummy reported on by Foster [1977] was the first to demonstrate human-like chest responses typical of the biomechanical data for frontal impacts. Rouhana [1989] developed a frangible abdomen, useful in predicting injury for lap-belt submarining. More recent work by Schneider [1992] led to a new prototype frontal dummy. Lateral impact tests of cadavers against a rigid wall and blunt pendulum led to side-impact dummies such as the Eurosid and Biosid [Mertz, 1993].

7.4 Injury Risk Assessment

Over years of study, tolerances have been established for most responses of the chest and abdomen. Table 7.1 provides tolerance levels from reviews by Cavanaugh [1993] and Rouhana [1993]. While these are single thresholds, they are commonly used to evaluate safety systems. The implication is that for biomechanical responses below tolerance there is no injury, and for responses above tolerance there is injury. An additional factor is biomechanical response scaling for individuals of different size and weight. The commonly accepted procedure involves equal stress and velocity, which enabled Mertz et al. [1989] to predict injury tolerances and biomechanical responses for different-sized adult dummies.

Injury risk assessment is frequently used. It evaluates the probability of injury as a continuous function of a biomechanical response. A logist function relates injury probability p to a biomechanical response x by p(x) = [1 + exp(α – βx)]–1, where α and β are parameters derived from statistical analysis of biomechanical data. This function provides a sigmoidal relationship with three distinct regions in Fig. 7.7. For low biomechanical response levels, there is a low probability of injury. Similarly, for very high levels, the risk asymptotes to 100%. The transition region between the two extremes involves risk that is proportional to the biomechanical response. A sigmoidal function is typical of human tolerance because it represents the distribution in weak through strong subjects in a population exposed to impact. Table 7.2 summarizes available parameters for chest and abdominal injury risk assessment.

TABLE 7.1 Human Tolerance for Chest and Abdomen Impact

Source: Adapted from Cavanaugh [1993] and Rouhana [1993].

FIGURE 7.7 Typical logist injury-probability function relating the risk of serious injury to the viscous response of the chest. (From Viano [1988]. With permission.)

TABLE 7.2 Injury Probability Functions for Blunt Impact

Source: Adapted from Viano [1989]. With permission.

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